Multiparticle Production in the Soft Limit and QCD Coherence

The production of gluons in a jet is considered in limited phase space, either with a cut in transverse momentum with respect to the jet axis $k_\perp<k_\perp^{cut}$ or with a cut in absolute momentum $|\vec{k} | <k^{cut}$. It is shown in the perturbative QCD calculations that in the soft limit $k_\perp^{cut} \to 0$ the multiplicity distribution becomes Poissonian, whereas for $k^{cut} \to 0$ the distribution remains non-Poissonian. The Poissonian limit is a consequence of the soft gluon coherence in the genuine multiparticle correlations. We also investigate how incoherent hadronization processes could possibly modify the predictions for small cut-off parameters.